Loading....
Coupon Accepted Successfully!

 
Series

A series is simply the sum of the terms of a sequence. The following is a series of even numbers formed from the sequence 2, 4, 6, 8, . . . :

2 + 4 + 6 + 8 + . . .


A term of a series is identified by its position in the series. In the above series, 2 is the first term, 4 is the second term, etc. The ellipsis symbol (. . .) indicates that the series continues forever.

 

Example 1:

The sum of the squares of the first n positive integers 1 2 + 22 + 32 +……+ n2 is nn+12n+16 . What is the sum of the squares of the first 9 positive integers?


(A) 90

(B) 125

(C) 200

(D) 285

(E) 682


We are given a formula for the sum of the squares of the first n positive integers. Plugging n = 9 into this formula yields

nn+12n+16 = 99+12·9+16 = 910196 = 285


The answer is (D).

 

Example 2:

For all integers x > 1, = 2x + (2x - 1) + (2x - 2)+……+2 + 1. What is the value of <3> · <2> ?


(A) 60

(B) 116

(C) 210

(D) 263

(E) 478


<3> = 2( 3) + (2 ·3 - 1) + (2 ·3 - 2) + (2 · 3 - 3) + (2 ·3 - 4) + (2· 3 - 5) = 6 + 5+ 4 + 3+ 2 + 1 = 21

<2> = 2( 2) + (2· 2 - 1) + (2· 2 - 2) + (2· 2 - 3) = 4 + 3 + 2 + 1= 10


Hence, <3>·<2> = 21·10 = 210, and the answer is (C).





Test Your Skills Now!
Take a Quiz now
Reviewer Name